ASI - they produce for large companies including New Era, Nike - Shanghai, China
Mainland Headwear - one of the larger factories, main office in Hong Kong, production in China
Yupong (famous for FlexFit hats), manufacture in China and Vietnam

I used to do performance apparel and all three of these can offer performance fabric options. All have snapback, flexible fit/flexfit, etc. Kevin @ Alterrapure.com